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Basis of Structural Design Course 1 Introduction to Structures Structural Materials Course notes are available for download at http://www.ct.upt.ro/users/AurelStratan/ Structures Man-made structures – – – – – – buildings bridges dams masts drilling platforms ships aircrafts, etc. Natural structures – – – – skeleton of animals shell of snails spider's web tree trunk and branches, etc. Structure: something which carries weight or resists loads and forces, and which may form a protective cover or skeleton for an object or living thing. 1 Some structures can fail 12.02.2009. Mall under construction in Oradea Some structures can fail 12.02.2009. Mall under construction in Oradea 2 Some structures can fail 12.02.2009. Mall under construction in Oradea Some structures can fail 12.02.2009. Mall under construction in Oradea 3 Some structures can fail 19.12.2008 – failure of a silo near Vinga Design criteria Suitability for its function: a building should be designed and realised in a manner that will offer to its users a certain function Safety and serviceability: – Structures should resist loads and other external actions without collapse, protecting its inhabitants – Structures should not develop excessive deformations and cracks, nor vibrate alarmingly Aesthetics: buildings should be aesthetically pleasant, both individually and as a group Economy: generally, the above three criteria need to be fulfilled with a limited budget – Cost to design and build a structure – Maintenance cost during the planned life 4 Structural materials A building consists of the structure and other components used in order to protect and provide for building function and aesthetics (cladding, partitions, floors, etc.) Structural material is the one which is used in those parts of the structure which carry loads and give it strength and stiffness Properties of . structural materials: – strength – stiffness – ductility . . deformation Structural materials: properties Strength (ultimate stress): the stress (load per unit area of the cross-section) at which the failure takes place – tension – compression Stiffness: the resistance of an elastic body to deformation Ductility: capacity of the material to deform into the inelastic range without significant loss of its load-bearing capacity force strength ductility stiffness deformation 5 Structural materials: ductility Ductile materials: able to deform significantly into the inelastic range Brittle materials: – fail suddenly by cracking or splintering – much weaker in tension than in compression force force ductile brittle deformation deformation Structural materials "Traditional" materials: used by builders and engineers since the ancient times Stone and timber: occur naturally Bricks: man-made – sun-dried clay/mud bricks - from 4500 B.C. – fired bricks - from 3000 B.C. – calcium silicate bricks Ancient concrete: – lime mixed with stone and sand: early civ. of the Middle East – "hydraulic cement" - lime, stone, sand and silicates: Romans Stone, bricks, ancient concrete: – weak – weaker in tension than in compression Stone and bricks masonry: units interconnected by even weaker mortar 6 Structural materials Timber: – substantial tensile strength along the grain – weak in compression and across the grain (difficult to realise connections in tension) "Modern" materials: Portland cement concrete, steel, aluminium , etc. Portland cement concrete: – mixture of Portland cement, water, aggregates – weaker in tension – brittle Steel (iron with low carbon content) and Aluminium (duraluminium alloy): – strong in tension and compression – ductile Structural materials: strength Material Traditional Granite Limestone Brick Along grain Timber (spruce) Across grain Modern Portland Normal use cement High strength concrete Mild steel High strength steel Iron and Very highsteel strength prestressing wires Aluminium alloy (dural) Stone Ultimate strength σu (N/mm2) Tensile Compression 40 200 5 40 6 60 120 30 3.5 2 20 6 60 355 355 700 700 2000 - 450 450 7 Specific strength All structures have to support their own weight Can the size of a structure be increased indefinitely for it to be able to carry its own weight? Problem: how long a bar of uniform cross-section can be before it breaks due to its own weight? Equate the weight of the bar to its tensile strength: Weight = Tensile resistance Specific strength Weight = Volume × specific weight W=A×L×ρ×g Tensile resistance = Area × ultimate tensile strength R = A × σu Equate weight to resistance: W = R ⇒ A × L × ρ × g = A × σu ⇒ L = σu / (ρ × g) = S = specific strength There is an absolute limit (= S) to the length that the bar can attain without breaking Larger a structure is, larger is the proportion of its own weight to the total load that can be carried by itself First to realise this: Galileo Galilei 8 Specific strength For structures subjected to tension/compression, as the size of an object increases, its strength increases with the square of the ruling dimensions, while the weight increases with its cube For each type of structure there is a maximum possible size beyond which it cannot carry even its own weight Consequences: – it is impossible to construct structures of enormous size – there is a limit to natural structures (trees, animals, etc.) – larger a structure becomes, stockier and more bulky it gets • large bridges are heavier in proportions than smaller ones • bones of elephants are stockier and thicker than the ones of mice – proportions of aquatic animals are almost unaffected by their size (weight is almost entirely supported by buoyancy) Specific strength Material Traditional Granite Stone Limestone Brick Along grain Timber (spruce) Across grain Modern Portland Normal use cement High strength concrete Mild steel High strength steel Iron and Very highsteel strength prestressing wires Aluminium alloy (dural) Ultimate strength σu (N/mm2) Tensile Compression 40 200 5 40 6 60 120 30 3.5 - Specific strength S (m) Tensile 1400 225 320 24000 700 Compression 7000 1800 3200 6000 - 2 20 90 900 6 60 270 2700 355 355 4500 4500 600 600 8000 8000 2000 - 26700 - 450 450 17000 17000 9 Specific strength Stone, brick and concrete: used in compression Steel: used in tension Timber: excellent performance in terms of specific strength, especially in tension Aluminium: high specific strength Aircrafts must carry loads and must be capable of being raised into the air under their own power ⇒ materials with high specific strength – wood was extensively used in early planes – modern material: aluminium Structural materials: stress-strain curves Stress-strain curves provide "at a glance" information on: – strength – stiffness – ductility Elastic region Inelastic region Steel: elastic region is almost linear Stone, brick, concrete, aluminium: elastic region is not linear 10 Structural materials: stress-strain curves Steel and aluminium: excellent ductility Concrete, brick: brittle Modulus of elasticity: E = σ / ε Unloading after loading in the elastic range ⇒ NO permanent deformations Unloading after loading in the inelastic range ⇒ permanent deformations present Permanent deformations need to be avoided in structures under service loads ⇒ stresses should be kept in the elastic region under service loads factor of safety = ultimate strength / design stress Structural materials: stiffness Excessive flexibility is undesirable in structures – people dislike noticeable vibration and deflections in buildings and bridges – large vibrations and deflections can damage (brittle) nonstructural components (partitions, glazing, floors, etc.) Materials with large stiffness are generally desirable (steel is more advantageous than aluminium from this point of view) Elastic efficiency of materials: – average stress in the bar: σ = A× ×L× ×ρ×g / (2A) = L× ×ρ×g / 2 – extension of the bar under its own weight δ = σ × L / E = L2×ρ×g / (2× ×E) = L2 / (2× ×M) – specific modulus of the material - a measure of material stiffness M = E / (ρ×g) the higher the value of M, the less it will extend under its own weight 11 Structural materials: stiffness The extension δ of a bar under its own weight is proportional to the square of the scale (a bar which is 10 times longer than a reference one will extend 102 = 100 times more than the reference one) Structural materials: stiffness and ductility Material Modulus of elasticity Specific modulus E (N/mm2) Ductility M (m ×10 × 5) Traditional Granite Limestone Brick Along grain Timber (spruce) Across grain 45 000 30 000 30 000 15 000 - 1.57 1.35 1.60 3.00 - Portland Normal use cement High strength concrete 25 000 1.12 40 000 1.80 210 000 2.80 210 000 2.80 210 000 2.80 Low ductility 70 000 2.80 Ductile Stone Mild steel Modern High strength Iron and steel steel Very highstrength prestressing wires Aluminium alloy (dural) Brittle NA Brittle Large ductility Moderate ductility 12 Structural materials: ductility Ductility is important for the "ultimate" behaviour of structures Most structures are designed to respond in the elastic range under service loads, but, given the uncertainties in real strength of material, behaviour of the structure, magnitude of loading, and accidental actions, a structure can be subjected to inelastic deformations A ductile material will sustain large deformations before collapsing, "warning" the people inside A ductile material allows for redistribution of stresses in statically indeterminate structures, which are able to support larger loads than in the case of a structure realised of brittle material 13